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A183955 Number of strings of numbers x(i=1..4) in 0..n with sum i^2*x(i) equal to n*16. 2

%I

%S 1,1,4,8,14,21,32,48,61,82,108,139,172,210,256,311,365,427,500,582,

%T 666,759,864,982,1097,1228,1372,1529,1688,1860,2048,2253,2457,2677,

%U 2916,3172,3430,3705,4000,4316,4629,4966,5324,5703,6084,6486,6912,7363,7813,8287

%N Number of strings of numbers x(i=1..4) in 0..n with sum i^2*x(i) equal to n*16.

%C Row 4 of A183953.

%H R. H. Hardin, <a href="/A183955/b183955.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) + a(n-16) - 2*a(n-17) + a(n-18) - a(n-20) + 2*a(n-21)-a(n-22).

%F Empirical g.f.: x*(1 - x + 3*x^2 + x^3 + x^4 + 2*x^5 + x^6 + 4*x^7 - 5*x^8 + 7*x^9 + x^10 + 5*x^12 - 3*x^13 + 3*x^14 + 4*x^15 - 4*x^16 + 4*x^17 - x^19 + 2*x^20 - x^21) / ((1 - x)^4*(1 + x)^2*(1 + x^2)^2*(1 + x^4)*(1 + x^8)). - _Colin Barker_, Apr 07 2018

%e All solutions for n=3:

%e ..2....3....0....1

%e ..3....1....0....1

%e ..2....1....0....3

%e ..1....2....3....1

%Y Cf. A183953.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 08 2011

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Last modified October 25 22:20 EDT 2021. Contains 348256 sequences. (Running on oeis4.)